Runge-Kutta neural network for identification of dynamical systems in high accuracy

This paper proposes Runge-Kutta neural networks (RKNNs) for identification of unknown dynamical systems described by ordinary differential equations (i.e., ordinary differential equation or ODE systems) with high accuracy. These networks are constructed according to the Runge-Kutta approximation method. The main attraction of the RKNNs is that they precisely estimate the changing rates of system states (i.e., the right-hand side of the ODE x =f(x)) directly in their subnetworks based on the space-domain interpolation within one sampling interval such that they can do long-term prediction of system state trajectories. We show theoretically the superior generalization and long-term prediction capability of the RKNNs over the normal neural networks. Two types of learning algorithms are investigated for the RKNNs, gradient-and nonlinear recursive least-squares-based algorithms. Convergence analysis of the learning algorithms is done theoretically. Computer simulations demonstrate the proved properties of the RKNNs.